Quantization of Nonstandard Hamiltonian Systems

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin-1/2 system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed nonstandard quantum theories.Comment: Revtex file, 23 pages, no figure

Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything else in the papper) on page 23 delete

Dynamics of test bodies with spin in de Sitter spacetime

We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma

Auditory perception in individuals with Friedreich’s Ataxia

INTRODUCTION: Friedreich's ataxia (FRDA) is an inherited ataxia with a range of progressive features including axonal degeneration of sensory nerves. The aim of this study was to investigate auditory perception in affected individuals. METHODS: Fourteen subjects with genetically defined FRDA participated. Two control groups, one consisting of healthy, normally hearing individuals and another comprised of subjects with sensorineural hearing loss, were also assessed. Auditory processing was evaluated using structured tasks designed to reveal the listeners' ability to perceive temporal and spectral cues. Findings were then correlated with open-set speech understanding. RESULTS: Nine of 14 individuals with FRDA showed evidence of auditory processing disorder. Gap and amplitude modulation detection levels in these subjects were significantly elevated, indicating impaired encoding of rapid signal changes. Electrophysiologic findings (auditory brainstem response, ABR) also reflected disrupted neural activity. Speech understanding was significantly affected in these listeners and the degree of disruption was related to temporal processing ability. Speech analyses indicated that timing cues (notably consonant voice onset time and vowel duration) were most affected. CONCLUSION: The results suggest that auditory pathway abnormality is a relatively common consequence of FRDA. Regular auditory evaluation should therefore be part of the management regime for all affected individuals. This assessment should include both ABR testing, which can provide insights into the degree to which auditory neural activity is disrupted, and some functional measure of hearing capacity such as speech perception assessment, which can quantify the disorder and provide a basis for interventio

Spacetime dynamics of spinning particles - exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers," a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec. 3.2.3 in the Supplement making connection to the post-Newtonian approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled) Supplement; references updated. The Supplement is provided in ancillary file. Matches the final published versio

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron

Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Ge

On spin-1 massive particles coupled to a Chern-Simons field

We study spin one particles interacting through a Chern-Simons field. In the Born approximation, we calculate the two body scattering amplitude considering three possible ways to introduce the interaction: (a) a Proca like model minimally coupled to a Chern-Simons field, (b) the model obtained from (a) by replacing the Proca's mass by a Chern-Simons term and (c) a complex Maxwell-Chern-Simons model minimally coupled to a Chern-Simons field. In the low energy regime the results show similarities with the Aharonov-Bohm scattering for spin 1/2 particles. We discuss the one loop renormalization program for the Proca's model. In spite of the bad ultraviolet behavior of the matter field propagator, we show that, up to one loop the model is power counting renormalizable thanks to the Ward identities satisfied by the interaction vertices.Comment: 14 pages, 5 figures, revte

Rotation and Spin in Physics

We delineate the role of rotation and spin in physics, discussing in order Newtonian classical physics, special relativity, quantum mechanics, quantum electrodynamics and general relativity. In the latter case, we discuss the generalization of the Kepler formula to post-Newtonian order $(c^{-2}$) including spin effects and two-body effects. Experiments which verify the theoretical results for general relativistic spin-orbit effects are discussed as well as efforts being made to verify the spin-spin effects

Chedoke Arm and Hand Activity Inventory-9 (CAHAI-9): Perceived clinical utility within 14 days of stroke

Purpose: The Chedoke Arm and Hand Activity Inventory-9 (CAHAI-9) is an activity-based assessment developed to include relevant functional tasks and to be sensitive to clinically important changes in upper limb function. The aim of this study was to explore both therapists' and clients' views on the clinical utility of CAHAI-9 within 14 days of stroke. Method: Twenty-one occupational therapists actively working in stroke settings were recruited by convenience sampling from 8 hospitals and participated in semistructured focus groups. Five clients within 14 days of stroke were recruited by consecutive sampling from 1 metropolitan hospital and participated in structured individual interviews. The transcripts were analyzed thematically. Results: Six themes emerged from the focus groups and interviews: collecting information, decisions regarding client suitability, administration and scoring, organizational demands, raising awareness, and clients' perceptions of CAHAI-9 utility. All therapists agreed CAHAI-9 was suited for the stroke population and assisted identification of client abilities or difficulties within functional contexts. Opinions varied as to whether CAHAI-9 should be routinely administered with clients who had mild and severe upper limb deficits, but therapists agreed it was appropriate for clients with moderate deficits. Therapists made suggestions regarding refinement of the scoring and training to increase utility. All clients with stroke felt that the assessment provided reassurance regarding their recovery. Conclusion: The findings indicate that CAHAI-9 shows promise as an upper limb ability assessment for clients within 14 days of stroke